A swaption (also known as a swap option) is an option to enter into an interest rate swap. A swaption has two key properties: the expiry and the tenor. Expiry defines the time interval in which one can enter into a swap, and tenor is the duration of the swap. Expiries can range from a few months to 30+ years while tenors are in the range of 1-30 years. This shows that there is a large variety of swaptions. To keep our analysis easy to interpret we chose a specific type of swaption with a 2-year tenor. We used historical data of GBP swaptions from ICAP (www.icap.com) with implied normal volatility values at 7 strike points (ATM (at-the-money strike) + [-50, -25, -12.5, 0.0, 12.5, 25, 50] bps (basis points) shifts) and at 7 expiries (9M, 1Y, 18M, 2Y, 3Y, 4Y and 5Y). Here, the implied normal volatility means the volatility that we should insert into the Bachelier pricing formula ([1]}) to reproduce the market prices. The observed time interval is between 2015 September 1 and 2020 October 21, hence we have volatility surface data for 1338 business days. It is worth mentioning that for swaptions the ATM strike value is different for each expiry, since it is calculated according to the forward curve. However, since we work in a "normal" (Bachelier) picture, without loss of generality, we can set all ATM values to zero, and search for possible paths that reproduce this market. Hence, in practice one should simply add the corresponding forward curve to the paths to calculate the price of other derivatives.
